A134763 a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).
1, 2, 4, 2, 16, 2, 58, 2, 208, 2, 754, 2, 2770, 2, 10294, 2, 38608, 2, 145858, 2, 554266, 2, 2116294, 2, 8112466, 2, 31201798, 2, 120349798, 2, 465352558, 2, 1803241168, 2, 7000818658, 2, 27225405898, 2, 106035791398, 2, 413539586458, 2, 1614773623318, 2, 6312296891158, 2
Offset: 0
Keywords
Examples
First few terms of the sequence are: (1, 2, 4, 2, 16, 2, 58, ...), interpolating two's in the sequence A134762: (1, 4, 16, 58, ...).
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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Magma
[3*((n+1) mod 2)*Binomial(n, Floor(n/2)) - 2*(-1)^n : n in [0..40]]; // G. C. Greubel, May 28 2024
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Mathematica
Table[(3/2)*(1+(-1)^n)*Binomial[n,n/2] -2*(-1)^n, {n,0,40}] (* G. C. Greubel, May 28 2024 *) -
SageMath
[3*((n+1)%2)*binomial(n, n//2) - 2*(-1)^n for n in range(41)] # G. C. Greubel, May 28 2024
Formula
From G. C. Greubel, May 28 2024: (Start)
a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).
a(n) = (3/2)*(1+(-1)^n)*A001405(n) - 2*(-1)^n.
G.f.: 3/sqrt(1-4*x^2) - 2/(1+x).
E.g.f.: 3*BesselI(0, 2*x) - 2*exp(-x). (End)
Extensions
Name change and terms a(14) onward added by G. C. Greubel, May 28 2024
Comments