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 A059722 a(n) = n*(2*n^2 - 2*n + 1). 14
 0, 1, 10, 39, 100, 205, 366, 595, 904, 1305, 1810, 2431, 3180, 4069, 5110, 6315, 7696, 9265, 11034, 13015, 15220, 17661, 20350, 23299, 26520, 30025, 33826, 37935, 42364, 47125, 52230, 57691, 63520, 69729, 76330, 83335, 90756, 98605, 106894, 115635, 124840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Mean of the first four nonnegative powers of 2n+1, i.e., ((2n+1)^0 + (2n+1)^1 + (2n+1)^2 + (2n+1)^3)/4. E.g., a(2) = (1 + 3 + 9 + 27)/4 = 10. Equatorial structured meta-diamond numbers, the n-th number from an equatorial structured n-gonal diamond number sequence. There are no 1- or 2-gonal diamonds, so 1 and (n+2) are used as the first and second terms since all the sequences begin as such. - James A. Record (james.record(AT)gmail.com), Nov 07 2004 Starting with offset 1 = row sums of triangle A143803. - Gary W. Adamson, Sep 01 2008 Form an array from the antidiagonals containing the terms in A002061 to give antidiagonals 1; 3,3; 7,4,7; 13,8,8,13; 21,14,9,14,21; and so on. The difference between the sum of the terms in n+1 X n+1 matrices and those in n X n matrices is a(n) for n>0. - J. M. Bergot, Jul 08 2013 Sum of the numbers from (n-1)^2 to n^2. - Wesley Ivan Hurt, Sep 08 2014 LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 Bruno Berselli, Table of sequences with the formula m*(m+1)^2 - (k+2)*m^2 (table includes this sequence for k = 2-m, m >= 0). Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = A053698(2*n-1)/4. a(n) = Sum_{j=1..n} ((n+j-1)^2-j^2+1). - Zerinvary Lajos, Sep 13 2006 From R. J. Mathar, Sep 02 2008: (Start) G.f.: x*(1 + x)*(1 + 5*x)/(1 - x)^4. a(n) = A002414(n-1) + A002414(n). a(n+1) - a(n) = A136392(n+1). (End) a(n) = (A000290(n) + A000290(n+1)) * (A000217(n+1) - A000217(n)). - J. M. Bergot, Nov 02 2012 a(n) = n * A001844(n-1). - Doug Bell, Aug 18 2015 a(n) = A000217(n^2) - A000217(n^2-2*n). - Bruno Berselli, Jun 26 2018 MAPLE A059722:=n->n*(2*n^2 - 2*n + 1): seq(A059722(n), n=0..50); # Wesley Ivan Hurt, Sep 08 2014 MATHEMATICA Table[n (2 n^2 - 2 n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Sep 08 2014 *) PROG (PARI) { for (n=0, 1000, write("b059722.txt", n, " ", n*(2*n^2 - 2*n + 1)); ) } \\ Harry J. Smith, Jun 28 2009 (MAGMA) [n*(2*n^2 - 2*n + 1) : n in [0..50]]; // Wesley Ivan Hurt, Sep 08 2014 CROSSREFS Cf. A000330, A005900, A081436, A100178, A100179, A059722: "equatorial" structured diamonds; A000447: "polar" structured meta-diamond; A006484 for other structured meta numbers; and A100145 for more on structured numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004 Cf. A000217, A059721, A059723. Cf. A143803. Sequence in context: A156674 A022277 A188480 * A267748 A229325 A074225 Adjacent sequences:  A059719 A059720 A059721 * A059723 A059724 A059725 KEYWORD nonn,easy AUTHOR Henry Bottomley, Feb 07 2001 EXTENSIONS Edited with new definition by N. J. A. Sloane, Aug 29 2008 STATUS approved

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Last modified May 27 03:03 EDT 2020. Contains 334647 sequences. (Running on oeis4.)