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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 A141631

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 April 18 12:34 EDT 2019. Contains 322209 sequences. (Running on oeis4.)