A024378 a(n) = 2nd elementary symmetric function of the first n+1 positive integers congruent to 1 mod 4.

5, 59, 254, 730, 1675, 3325, 5964, 9924, 15585, 23375, 33770, 47294, 64519, 86065, 112600, 144840, 183549, 229539, 283670, 346850, 420035, 504229, 600484, 709900, 833625, 972855, 1128834, 1302854, 1496255, 1710425, 1946800, 2206864, 2492149, 2804235, 3144750, 3515370

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Formula

a(n) = n*(n+1)*(12*n^2+8*n-5)/6.

G.f.: -x*(5+34*x+9*x^2) / (x-1)^5. - R. J. Mathar, Oct 08 2011

Maple

A024378:=n->n*(n+1)*(12*n^2+8*n-5)/6: seq(A024378(n), n=1..50); # Wesley Ivan Hurt, Apr 27 2017

Mathematica

A024378[n_] := n*(n + 1)*(4*n*(3*n + 2) - 5)/6; Array[A024378, 50] (* Paolo Xausa, May 20 2026 *)

Crossrefs

Sequence in context: A179028 A179029 A049079 * A362535 A112461 A386071

Adjacent sequences: A024375 A024376 A024377 * A024379 A024380 A024381

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Paolo Xausa, May 20 2026

Status

approved