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 A198392 a(n) = (6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16 + 1. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 26 07:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)