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A376330

Decimal expansion of 1 bit in J/K.

+0
0

9, 5, 6, 9, 9, 2, 9, 6, 1, 6, 9, 2, 9, 0, 7, 9, 3, 1, 5, 0, 1, 5, 9, 2, 1, 1, 1, 2, 5, 9, 1, 1, 0, 0, 2, 0, 5, 3, 6, 8, 7, 1, 1, 8, 5, 0, 0, 4, 3, 5, 2, 0, 5, 6, 3, 4, 6, 4, 6, 2, 7, 3, 4, 4, 2, 7, 0, 4, 4, 4, 1, 0, 7, 7, 8, 8, 3, 7, 0, 3, 9, 4, 0, 6, 5, 1, 9

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

-23,1

LINKS

Table of n, a(n) for n=-23..63.

Index entries for transcendental numbers

FORMULA

Exactly equal to log(2) * 1.380649 * 10^-23 under the 2019 SI redefinition.

EXAMPLE

9.569929616929079315015921112591100205368711850043520563464627344270444107788370394 * 10^-24 J/K.

PROG

(PARI) 1.380649e-23*log(2) \\ Charles R Greathouse IV, Sep 20 2024

CROSSREFS

Cf. A070063.

KEYWORD

cons,nonn,new

AUTHOR

Charles R Greathouse IV, Sep 20 2024

STATUS

approved

A376335

Irregular triangle read by rows: T(n,k) = A008949(n-1,k) if 0 <= k <= n - 2 otherwise A008949(n-1,2*n-4-k) if n - 2 <= k <= 2*n - 4.

+0
0

1, 1, 3, 1, 1, 4, 7, 4, 1, 1, 5, 11, 15, 11, 5, 1, 1, 6, 16, 26, 31, 26, 16, 6, 1, 1, 7, 22, 42, 57, 63, 57, 42, 22, 7, 1, 1, 8, 29, 64, 99, 120, 127, 120, 99, 64, 29, 8, 1, 1, 9, 37, 93, 163, 219, 247, 255, 247, 219, 163, 93, 37, 9, 1, 1, 10, 46, 130, 256, 382, 466, 502, 511, 502, 466, 382, 256, 130, 46, 10, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Table of n, a(n) for n=2..82.

Nsibiet E. Udo, Praise Adeyemo, Balazs Szendroi, and Stavros Argyrios Papadakis, Ideals, representations and a symmetrised Bernoulli triangle, arXiv:2409.10278 [math.AC], 2024. See p. 2.

FORMULA

Sum_{k=0..2*n-4} T(n,k) = A000337(n-1). [Udo et al.]

EXAMPLE

The triangle begins as:

1, 3, 1;

1, 4, 7, 4, 1;

1, 5, 11, 15, 11, 5, 1;

1, 6, 16, 26, 31, 26, 16, 6, 1;

1, 7, 22, 42, 57, 63, 57, 42, 22, 7, 1;

...

MATHEMATICA

b[n_, k_]:=Sum[Binomial[n, j], {j, 0, k}]; T[n_, k_]:=If[0<=k<=n-2, b[n-1, k], b[n-1, 2n-4-k]]; Table[T[n, k], {n, 2, 10}, {k, 0, 2n-4}]//Flatten

CROSSREFS

Cf. A000337, A008949.

KEYWORD

nonn,easy,tabf,new

AUTHOR

Stefano Spezia, Sep 20 2024

STATUS

approved

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