A222408 Partial sums of A008531, or crystal ball sequence for {A_4}* lattice.

1, 11, 61, 211, 551, 1201, 2311, 4061, 6661, 10351, 15401, 22111, 30811, 41861, 55651, 72601, 93161, 117811, 147061, 181451, 221551, 267961, 321311, 382261, 451501, 529751, 617761, 716311, 826211, 948301, 1083451

Offset: 0

Author

N. J. A. Sloane, Feb 21 2013

Keywords

• nonn
• easy
• changed

Links

• Ben Thurston, 2-dimensional model of initial terms (cf. A001846)
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A008531, A001846.

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{1,11,61,211,551},40] (* Harvey P. Dale, Aug 22 2025 *)

PARI

a(n)=5*n*(n+1)*(n^2+n+2)/4 \\ Charles R Greathouse IV, Mar 08 2013

Formula

a(n) = (4+10*n+15*n^2+10*n^3+5*n^4)/4. G.f.: -(x^4+6*x^3+16*x^2+6*x+1) / (x-1)^5. [Colin Barker, Mar 08 2013]