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 A064808 The (n+1)st (n+2)-gonal number. 18
 1, 3, 9, 22, 45, 81, 133, 204, 297, 415, 561, 738, 949, 1197, 1485, 1816, 2193, 2619, 3097, 3630, 4221, 4873, 5589, 6372, 7225, 8151, 9153, 10234, 11397, 12645, 13981, 15408, 16929, 18547, 20265, 22086, 24013, 26049, 28197, 30460, 32841, 35343, 37969, 40722 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of n terms of the arithmetic progression with first term 1 and common difference n-1. - Amarnath Murthy, Aug 04 2005 a(n) = sum of row (n+1)-th row terms of triangle A144693. - Gary W. Adamson, Sep 19 2008 See also A131685(k) = smallest positive number m such that c(i) = m (i^1 + 1) (i^2 + 2) ... (i^k+ k) / k! takes integral values for all i>=0: For k=2, A131685(k)=1, which implies that this is a well-defined integer sequence. - Alexander R. Povolotsky, Apr 24 2015 LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (n + 1)*(n^2 + 2)/2. From Paul Barry, Nov 18 2005: (Start) a(n) = Sum_{k=0..n} Sum_{j=0..n} (k-(k-1)*C(0, j-k)). a(n) = A006002(n) - A000096(n-2). (End) G.f.: (1 - x + 3x^2)/(1 - x)^4. - R. J. Mathar, Jul 07 2009 a(n) = A006003(n+1) - A002378(n). - Rick L. Shepherd, Feb 21 2015 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, Feb 21 2015 a(n) = A057145(n+2,n+1). - R. J. Mathar, Jul 28 2016 MAPLE A064808:=n->(n+1)*(n^2+2)/2: seq(A064808(n), n=0..50); # Wesley Ivan Hurt, Feb 21 2015 MATHEMATICA Table[(n + 1) (n^2 + 2)/2, {n, 0, 50}] (* Wesley Ivan Hurt, Feb 21 2015 *) PROG (PARI) { for (n=0, 1000, write("b064808.txt", n, " ", (n + 1)*(n^2 + 2)/2) ) } \\ Harry J. Smith, Sep 26 2009 (MAGMA) [(n+1)*(n^2+2)/2 : n in [0..50]]; // Wesley Ivan Hurt, Feb 21 2015 CROSSREFS Main diagonal of A057145. Row sums of A076110. Cf. A144693. - Gary W. Adamson, Sep 19 2008 Cf. A000096, A002378, A006002, A006003. Sequence in context: A063586 A131477 A002128 * A223718 A217882 A217881 Adjacent sequences:  A064805 A064806 A064807 * A064809 A064810 A064811 KEYWORD nonn,easy AUTHOR Floor van Lamoen, Oct 22 2001 STATUS approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)