A198392 a(n) = (6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16 + 1.

2, 4, 12, 18, 31, 41, 59, 73, 96, 114, 142, 164, 197, 223, 261, 291, 334, 368, 416, 454, 507, 549, 607, 653, 716, 766, 834, 888, 961, 1019, 1097, 1159, 1242, 1308, 1396, 1466, 1559, 1633, 1731, 1809, 1912, 1994, 2102, 2188, 2301, 2391, 2509, 2603, 2726, 2824, 2952

Offset

0,1

Comments

For an origin of this sequence, see the triangular spiral illustrated in the Links section.

First bisection gives A117625 (without the initial term).

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Bruno Berselli, Illustration of initial terms.

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

Formula

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).

a(n)-a(-n-1) = A168329(n+1).

a(n)+a(n-1) = A102214(n).

a(2n)-a(2n-1) = A016885(n).

a(2n+1)-a(2n) = A016825(n).

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {2, 4, 12, 18, 31}, 60] (* Harvey P. Dale, Jun 15 2022 *)

Prog

(PARI) for(n=0, 50, print1((6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1", "));
(Magma) [(6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1: n in [0..50]];

Crossrefs

Cf. A152832 (by Superseeker).

Cf. sequences related to the triangular spiral: A022266, A022267, A027468, A038764, A045946, A051682, A062708, A062725, A062728, A062741, A064225, A064226, A081266-A081268, A081270-A081272, A081275 [incomplete list].

Sequence in context: A303403 A064407 A309519 * A052289 A309547 A309552

Adjacent sequences: A198389 A198390 A198391 * A198393 A198394 A198395

Keyword

nonn,easy

Author

Bruno Berselli, Oct 25 2011

Status

approved