A106113 5th diagonal of triangle in A059317.

0, 0, 0, 1, 8, 29, 72, 146, 261, 428, 659, 967, 1366, 1871, 2498, 3264, 4187, 5286, 6581, 8093, 9844, 11857, 14156, 16766, 19713, 23024, 26727, 30851, 35426, 40483, 46054, 52172, 58871, 66186, 74153, 82809, 92192, 102341, 113296, 125098, 137789, 151412

Offset

0,5

Links

Table of n, a(n) for n=0..41.

W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

For n>2, a(n) = (1/24) [n^4 + 14n^3 - 97n^2 + 154n - 24 ].

From Chai Wah Wu, Mar 11 2021: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.

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

Prog

(PARI) a(n)=if(n>2, n^4 + 14*n^3 - 97*n^2 + 154*n - 24, 0)/24 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Sequence in context: A037157 A288115 A100178 * A362153 A299260 A290312

Adjacent sequences: A106110 A106111 A106112 * A106114 A106115 A106116

Keyword

nonn,easy

Author

N. J. A. Sloane, May 28 2005

Status

approved