A329530 a(n) = n * (7*binomial(n, 2) + 1).

0, 1, 16, 66, 172, 355, 636, 1036, 1576, 2277, 3160, 4246, 5556, 7111, 8932, 11040, 13456, 16201, 19296, 22762, 26620, 30891, 35596, 40756, 46392, 52525, 59176, 66366, 74116, 82447, 91380, 100936, 111136, 122001, 133552, 145810, 158796, 172531, 187036, 202332, 218440

Offset: 0

Author

Ilya Gutkovskiy, Nov 15 2019

Keywords

• nonn
• easy

Comments

Centered heptagonal prism numbers.

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), 144.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Centered m-gonal prism numbers: A100175 (m = 3), A059722 (m = 4), A006564 (m = 5), A005915 (m = 6), this sequence (m = 7), A139757 (m = 8), A006566 (m = 9).

Cf. A000217, A002413, A006597, A024966, A069099.

Programs

Mathematica

Table[n (7 Binomial[n, 2] + 1), {n, 0, 40}]
nmax = 40; CoefficientList[Series[x (1 + 12 x + 8 x^2)/(1 - x)^4, {x, 0, nmax}], x]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 16, 66}, 41]

Formula

G.f.: x * (1 + 12*x + 8*x^2) / (1 - x)^4.

E.g.f.: exp(x) * x * (2 + 14*x + 7*x^2) / 2.

a(n) = n * (7*n^2 - 7*n + 2) / 2.

a(n) = n * (7*A000217(n-1) + 1).

a(n) = n * A069099(n).