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 A220083 a(n) = (15*n^2 + 9*n + 2)/2. 8
 1, 13, 40, 82, 139, 211, 298, 400, 517, 649, 796, 958, 1135, 1327, 1534, 1756, 1993, 2245, 2512, 2794, 3091, 3403, 3730, 4072, 4429, 4801, 5188, 5590, 6007, 6439, 6886, 7348, 7825, 8317, 8824, 9346, 9883, 10435, 11002, 11584, 12181, 12793, 13420, 14062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence related to the heptagonal numbers (A000566) by a(n) = n*A000566(n)-(n-1)*A000566(n-1). Other similar sequences: A005408(m) = (m+1)*A001477(m+1)-m*A001477(m), A001477 = nonn. integers; A000326(m) = m*A000217(n)-(m-1)*A000217(m-1), A000217 = triangular numbers; A003215(m) = (m+1)*A000290(m+1)-n*A000290(m), A000290 = square numbers; A081267(m) = (m+1)*A000326(m+1)-n*A000326(m), A000326 = pentagonal numbers; A080859(m) = (m+1)*A000384(m+1)-n*A000384(m), A000384 = hexagonal numbers; A214675(m) = m*A000567(m)-(m-1)*A000567(m-1), A000567 = octagonal numbers. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1+10*x+4*x^2)/(1-x)^3. Sum( a(i), i=0..n ) = A006597(n+1). a(n) + a(-n) = A010005(n) for n>0. MAPLE A220083:=n->(15*n^2 + 9*n + 2)/2; seq(A220083(n), n=0..100); # Wesley Ivan Hurt, Nov 14 2013 MATHEMATICA Table[(15 n^2 + 9 n + 2)/2, {n, 0, 45}] CoefficientList[Series[(1 + 10 x + 4 x^2) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *) PROG (MAGMA) /* By first comment: */  A000566:=func; [n*A000566(n)-(n-1)*A000566(n-1): n in [1..45]]; (MAGMA) [(15*n^2 + 9*n + 2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 18 2013 (Maxima) A220083(n):=(15*n^2 + 9*n + 2)/2\$ makelist(A220083(n), n, 0, 20); /* Martin Ettl, Dec 11 2012 */ (PARI) a(n)=(15*n^2+9*n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000326, A003215, A005408, A006597, A080859, A081267, A214675. Sequence in context: A258597 A299816 A041324 * A041326 A319088 A041755 Adjacent sequences:  A220080 A220081 A220082 * A220084 A220085 A220086 KEYWORD nonn,easy AUTHOR Bruno Berselli, Dec 10 2012 STATUS approved

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Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)