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 A064694 Add column entries of the table with rows (1,2,0,0...), (0,3,4,5,0,0...), (0,0,6,7,8,9,0,0...), (0,0,0,10,11,12,13,14,0,0...), ... 2
 1, 5, 10, 22, 34, 58, 80, 120, 155, 215, 266, 350, 420, 532, 624, 768, 885, 1065, 1210, 1430, 1606, 1870, 2080, 2392, 2639, 3003, 3290, 3710, 4040, 4520, 4896, 5440, 5865, 6477, 6954, 7638, 8170, 8930, 9520, 10360, 11011, 11935, 12650, 13662, 14444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Harry J. Smith, Table of n, a(n) for n=1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). FORMULA a(2n-1) = n*(n+1)*(7*n-4)/6 (see A007584), a(2n) = n*(n+1)*(7*n+8)/6. a(n) = sum{k=0..floor((n+1)/2), (n-k+1)ceiling((n-k+1)/2)+k+if(mod(n-k+1, 2) =0, ceiling((n-k+1)/2), 0)}. - Paul Barry, Aug 25 2004 a(n) = sum{k=0..floor(n/2), C(n-k+1,2)+k}; - Paul Barry, Jul 23 2008 a(n) = (2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(14*n+15+17*(-1)^n)/384. - Luce ETIENNE, Feb 17 2015 From Colin Barker, Feb 17 2015: (Start) a(n) = (7*n^3+30*n^2+32*n)/48 for n even. a(n) = (7*n^3+27*n^2+17*n-3)/48 for n odd. G.f.: x*(2*x^2+4*x+1) / ((x-1)^4*(x+1)^3). (End) EXAMPLE a(1)=1, a(2)=2+3=5, a(3)=4+6=10, a(4)=5+7+10=22. MATHEMATICA Table[ Sum[ Binomial[n-k+1, 2] + k, {k, 0, Floor[n/2]}], {n, 1, 45}] (* Jean-François Alcover, Sep 16 2013 *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 5, 10, 22, 34, 58, 80}, 50] (* Harvey P. Dale, Dec 11 2015 *) PROG (PARI) { for (n=1, 1000, a=sum(k=0, n\2, binomial(n - k + 1, 2) + k); write("b064694.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 22 2009 (PARI) Vec(x*(2*x^2+4*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Feb 17 2015 CROSSREFS Cf. A007584. Sequence in context: A271257 A343456 A087746 * A264147 A229440 A067622 Adjacent sequences: A064691 A064692 A064693 * A064695 A064696 A064697 KEYWORD nonn,easy,nice AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 12 2001 STATUS approved

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Last modified June 10 17:56 EDT 2023. Contains 363206 sequences. (Running on oeis4.)