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A186424 Odd terms in A186423. 9
1, 3, 11, 17, 33, 43, 67, 81, 113, 131, 171, 193, 241, 267, 323, 353, 417, 451, 523, 561, 641, 683, 771, 817, 913, 963, 1067, 1121, 1233, 1291, 1411, 1473, 1601, 1667, 1803, 1873, 2017, 2091, 2243, 2321, 2481, 2563, 2731, 2817, 2993, 3083, 3267, 3361, 3553, 3651 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sum of odd square and half of even square. - Vladimir Joseph Stephan Orlovsky, May 20 2011

Numbers m such that 6*m-2 is a square. - Bruno Berselli, Apr 29 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f. ( -1-2*x-6*x^2-2*x^3-x^4 ) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Feb 28 2011

a(n) = 3*(1+2*n+2*n^2)/4 + (-1)^n*(1+2*n)/4. - R. J. Mathar, Feb 28 2011

a(n+2) = a(n) + A091999(n+2).

Union of A080859 and A126587: a(2*n) = A080859(n) and a(2*n+1) = A126587(n+1).

MATHEMATICA

Table[If[OddQ[n], n^2+((n+1)^2)/2, (n^2)/2+(n+1)^2], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)

PROG

(Haskell)

a186424 n = a186424_list !! n

a186424_list = filter odd a186423_list

CROSSREFS

Cf. A186421.

Sequence in context: A194800 A154501 A045432 * A018520 A154933 A197225

Adjacent sequences:  A186421 A186422 A186423 * A186425 A186426 A186427

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Feb 21 2011

STATUS

approved

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Last modified November 25 11:32 EST 2020. Contains 338623 sequences. (Running on oeis4.)