A373733 Triangular numbers with tetrahedral indices: a(n) = (1/72) * (n*(n+1)*(n+2)*(n+3)*(n^2+2)).
0, 1, 10, 55, 210, 630, 1596, 3570, 7260, 13695, 24310, 41041, 66430, 103740, 157080, 231540, 333336, 469965, 650370, 885115, 1186570, 1569106, 2049300, 2646150, 3381300, 4279275, 5367726, 6677685, 8243830, 10104760, 12303280
Offset: 0
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Mathematica
PolygonalNumber[Binomial[Range[2, 50], 3]] (* Paolo Xausa, Jul 22 2024 *)
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PARI
a(n)=n*(n+1)*(n+2)*(n+3)*(n^2+2)/72 \\ Charles R Greathouse IV, Jul 10 2024
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Python
from math import comb def A373733(n): return comb(comb(n+2,3)+1,2) # Chai Wah Wu, Jul 10 2024