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 A081436 Diagonal in array of n-gonal numbers A081422. 25
 1, 7, 24, 58, 115, 201, 322, 484, 693, 955, 1276, 1662, 2119, 2653, 3270, 3976, 4777, 5679, 6688, 7810, 9051, 10417, 11914, 13548, 15325, 17251, 19332, 21574, 23983, 26565, 29326, 32272, 35409, 38743, 42280, 46026, 49987, 54169, 58578, 63220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS One of a family of sequences with palindromic generators. Also as A(n) = (1/6)*(6*n^3 - 3*n^2 + 3*n), n>0: structured pentagonal diamond numbers (vertex structure 5). (Cf. A004068 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.) - James A. Record (james.record(AT)gmail.com), Nov 07 2004 Sequence of the absolute values of the z^1 coefficients of the polynomials in the GF4 denominators of A156933. See A157705 for background information. - Johannes W. Meijer, Mar 07 2009 Row 1 of the convolution arrays A213831 and A213833. - Clark Kimberling, Jul 04 2012 Partial sums of A056109. - J. M. Bergot, Jun 22 2013 Number of ordered pairs of intersecting multisets of size 2, each chosen with repetition from {1,...,n}. - Robin Whitty, Feb 12 2014 Row sums of A244418. - L. Edson Jeffery, Jan 10 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 J. A. Dias da Silva and P. J. Freitas, Counting Spectral Radii of Matrices with Positive Entries, arXiv:1305.1139 [math.CO], 2013. Theorem of the Day, Lovász Local Lemma example involving intersecting pairs of multisets Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (n+1)*(2*n^2 + 3*n + 2)/2. G.f.: (1+x)*(1+2*x)/(1-x)^4. (Convolution of A005408 and A016777.) a(n) = A110449(n, n-1), for n>1. a(n) = (n+1)*T(n+1) + n*T(n), where T( ) are triangular numbers. Binomial transform of [1, 6, 11, 6, 0, 0, 0,...]. - Gary W. Adamson, Dec 28 2007 MAPLE A081436 := proc(n)     (n+1)*(2*n^2+3*n+2)/2 ; end proc: seq(A081436(n), n=0..60) ; # R. J. Mathar, Jun 26 2013 MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {1, 7, 24, 58}, 40] (* Jean-François Alcover, Sep 21 2017 *) PROG (MAGMA) [(2*n^3+5*n^2+5*n+2)/2: n in [0..40]]; // Vincenzo Librandi, Jul 19 2011 (PARI) a(n)=n^3+5/2*n*(n+1)+1 \\ Charles R Greathouse IV, Jun 20 2013 (Sage) [(n+1)*(2*(n+1)^2-n)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019 (GAP) List([0..40], n-> (n+1)*(2*(n+1)^2-n)/2); # G. C. Greubel, Aug 14 2019 CROSSREFS Cf. A081434, A081435, A081437, A156933, A157705, A244418. Sequence in context: A079671 A212511 A100454 * A024205 A008779 A062449 Adjacent sequences:  A081433 A081434 A081435 * A081437 A081438 A081439 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 21 2003 EXTENSIONS G.f. simplified and crossrefs added by Johannes W. Meijer, Mar 07 2009 STATUS approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)