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 A074377 Generalized 10-gonal numbers: m*(4*m - 3) for m = 0, +- 1, +- 2, +- 3, ... 80
 0, 1, 7, 10, 22, 27, 45, 52, 76, 85, 115, 126, 162, 175, 217, 232, 280, 297, 351, 370, 430, 451, 517, 540, 612, 637, 715, 742, 826, 855, 945, 976, 1072, 1105, 1207, 1242, 1350, 1387, 1501, 1540, 1660, 1701, 1827, 1870, 2002, 2047, 2185, 2232, 2376, 2425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also called generalized decagonal numbers. Odd triangular numbers decremented and halved. It appears that this is zero together with the partial sums of A165998. - Omar E. Pol, Sep 10 2011 [this is correct, see the g.f., Joerg Arndt, Sep 29 2013] Also, A033954 and positive members of A001107 interleaved. - Omar E. Pol, Aug 04 2012 Also, numbers m such that 16*m+9 is a square. After 1, therefore, there are no squares in this sequence. - Bruno Berselli, Jan 07 2016 Convolution of the sequences A047522 and A059841. - Ilya Gutkovskiy, Mar 16 2017 Numbers k such that the concatenation k5625 is a square. - Bruno Berselli, Nov 07 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Neville Holmes, More Gemometric Integer Sequences [Broken link] Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA (n(n+1)-2)/4 where n(n+1)/2 is odd. G.f.: x*(1+6*x+x^2)/((1-x)*(1-x^2)^2). - Michael Somos, Mar 04 2003 a(2*k) = k*(4*k+3); a(2*k+1) = (2*k+1)^2+k. - Benoit Jubin, Feb 05 2009 a(n) = n^2+n-1/4+(-1)^n/4+n*(-1)^n/2. - R. J. Mathar, Oct 08 2011 Sum_{n>=1} 1/a(n) = (4 + 3*Pi)/9. - Vaclav Kotesovec, Oct 05 2016 E.g.f.: exp(x)*x^2 + (2*exp(x) - exp(-x)/2)*x - sinh(x)/2. - Ilya Gutkovskiy, Mar 16 2017 MATHEMATICA CoefficientList[Series[x(1 +6x +x^2)/((1-x)(1-x^2)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 29 2013 *) LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 7, 10, 22}, 50] (* G. C. Greubel, Nov 07 2018 *) PROG (PARI) a(n)=(2*n+3-4*(n%2))*(n-n\2) (PARI) concat([0], Vec(x*(1 + 6*x + x^2)/((1 - x)*(1 - x^2)^2) +O(x^50))) \\ Indranil Ghosh, Mar 16 2017 (MAGMA) [n^2+n-1/4+(-1)^n/4+n*(-1)^n/2: n in [0..50]]; // Vincenzo Librandi, Sep 29 2013 CROSSREFS Cf. A011848, A014493, A074378, A118277, A165998. Cf. A001107 (10-gonal numbers). Column 6 of A195152. Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), this sequence (k=10), A195160 (k=11), A195162 (k=12), A195313 (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30). Cf. sequences of the form m*(m+k)/(k+1) listed in A274978. [Bruno Berselli, Jul 25 2016] Sequence in context: A327977 A097634 A120312 * A103119 A054224 A183330 Adjacent sequences:  A074374 A074375 A074376 * A074378 A074379 A074380 KEYWORD nonn,easy AUTHOR W. Neville Holmes, Sep 04 2002 EXTENSIONS New name from T. D. Noe, Apr 21 2006 Formula in sequence name from Omar E. Pol, May 28 2012 STATUS approved

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Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)