A239592 a(n) = (n^4 - n^3 + 4*n^2 + 2)/2.

1, 3, 13, 46, 129, 301, 613, 1128, 1921, 3079, 4701, 6898, 9793, 13521, 18229, 24076, 31233, 39883, 50221, 62454, 76801, 93493, 112773, 134896, 160129, 188751, 221053, 257338, 297921, 343129, 393301, 448788, 509953, 577171, 650829, 731326, 819073, 914493

Offset: 0

Author

Philippe Deléham, Mar 22 2014

Keywords

• nonn
• easy

Comments

Main diagonal of square array A239331.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A239331.

Programs

Magma

[(n^4-n^3+4*n^2 + 2)/2: n in [0..40]]; // Vincenzo Librandi, Mar 23 2014

Mathematica

CoefficientList[Series[(1 - 2 x + 8 x^2 + x^3 + 4 x^4)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)

PARI

Vec((1-2*x+8*x^2+x^3+4*x^4)/(1-x)^5 + O(x^100)) \\ Colin Barker, Mar 22 2014

Formula

G.f.: (1 - 2*x + 8*x^2 + x^3 + 4*x^4)/(1-x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), a(0) = 1, a(1) = 3, a(2) = 13, a(3) = 46, a(4) = 129.

a(n) = A058331(n) + A092364(n).