A342362 Expansion of the o.g.f. (1 + 8*x + 10*x^2 + 8*x^3 + x^4)/((1 - x)^4*(1 + x)^2).

1, 10, 31, 76, 145, 254, 399, 600, 849, 1170, 1551, 2020, 2561, 3206, 3935, 4784, 5729, 6810, 7999, 9340, 10801, 12430, 14191, 16136, 18225, 20514, 22959, 25620, 28449, 31510, 34751, 38240, 41921, 45866, 50015, 54444, 59089, 64030, 69199, 74680, 80401, 86450, 92751, 99396, 106305, 113574

Offset: 0

Author

Petros Hadjicostas, Mar 09 2021

Keywords

• nonn
• easy

Comments

Antidiagonal sums of square array A342354.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A342354.

Programs

Julia

[div((n + 1)*(14*(n + 1)^2 - 3*(-1)^n + 1),12) for n in 0:50] |> println # Bruno Berselli, Mar 09 2021

Formula

a(n) = (n + 1)/4*(5 - (-1)^n) - 7*binomial(n + 2, 2) + 7*binomial(n + 3, 3).

a(n) = (n + 1)*(14*(n + 1)^2 - 3*(-1)^n + 1)/12. - Bruno Berselli, Mar 09 2021