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 A195605 a(n) = (4*n*(n+2)+(-1)^n+1)/2 + 1. 6
 2, 7, 18, 31, 50, 71, 98, 127, 162, 199, 242, 287, 338, 391, 450, 511, 578, 647, 722, 799, 882, 967, 1058, 1151, 1250, 1351, 1458, 1567, 1682, 1799, 1922, 2047, 2178, 2311, 2450, 2591, 2738, 2887, 3042, 3199, 3362, 3527, 3698, 3871, 4050, 4231, 4418, 4607, 4802 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sequence found by reading the numbers in increasing order on the vertical line containing 2 of the square spiral whose vertices are the triangular numbers (A000217) - see Pol's comments in other sequences visible in this numerical spiral. Also A077591 (without first term) and A157914 interleaved. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Bruno Berselli, Illustration of initial terms: An origin of A195605. Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: (2+3*x+4*x^2-x^3)/((1+x)*(1-x)^3). a(n) = a(-n-2) = 2*a(n-1)-2*a(n-3)+a(n-4). a(n) = A047524(A000982(n+1)). MATHEMATICA CoefficientList[Series[(2 + 3 x + 4 x^2 - x^3) / ((1 + x) (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *) LinearRecurrence[{2, 0, -2, 1}, {2, 7, 18, 31}, 50] (* Harvey P. Dale, Jan 21 2017 *) PROG (MAGMA) [(4*n*(n+2)+(-1)^n+3)/2: n in [0..48]]; (PARI) for(n=0, 48, print1((4*n*(n+2)+(-1)^n+3)/2", ")); CROSSREFS Cf. A000217. Cf. A047621 (contains first differences), A016754 (contains the sum of any two consecutive terms). Cf. A033585, A069129, A077221, A102083, A139098, A139271-A139277, A139592, A139593, A188135, A194268, A194431, A195241 [incomplete list]. Sequence in context: A301325 A001114 A107615 * A184096 A136583 A307684 Adjacent sequences:  A195602 A195603 A195604 * A195606 A195607 A195608 KEYWORD nonn,easy AUTHOR Bruno Berselli, Sep 21 2011 - based on remarks and sequences by Omar E. Pol. STATUS approved

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)