The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049778 a(n) = Sum_{k=1..floor((n+1)/2)} T(n,2k-1), array T as in A049777. 5
 1, 3, 9, 17, 32, 50, 78, 110, 155, 205, 271, 343, 434, 532, 652, 780, 933, 1095, 1285, 1485, 1716, 1958, 2234, 2522, 2847, 3185, 3563, 3955, 4390, 4840, 5336, 5848, 6409, 6987, 7617, 8265, 8968, 9690, 10470, 11270, 12131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Principal diagonal of the convolution array A213849. - Clark Kimberling, Jul 04 2012 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA G.f.: x*(1 + x + 2*x^2)/((1-x)^4*(1+x)^2). Pairwise sums of A023855. - Ralf Stephan, May 06 2004 a(n) = Sum_{k=1..n} k*ceiling(k/2). - Vladeta Jovovic, Apr 29 2006 Row sums of triangle A095800^2. - Gary W. Adamson, Dec 12 2007 a(n) = (3 + 10*n + 18*n^2 + 8*n^3 - 3*(-1)^n*(1 + 2*n))/48. - R. J. Mathar, Mar 03 2011 From G. C. Greubel, Dec 12 2019: (Start) a(n) = m*(3*(n-1)*(n+2) - (m+1)*(4*m-7))/6, where m = floor((n+1)/2). E.g.f.: ( (3+36*x+42*x^2+8*x^3)*exp(x) - 3*(1-2*x)*exp(-x) )/48. (End) MAPLE seq( (3 +10*n +18*n^2 +8*n^3 -3*(-1)^n*(1+2*n))/48, n=1..50); # G. C. Greubel, Dec 12 2019 MATHEMATICA Table[Floor[(n+1)/2]*(3*(n-1)*(n+2) -(1+Floor[(n+1)/2])*(4*Floor[(n+1)/2]-7))/6, {n, 50}] (* G. C. Greubel, Dec 12 2019 *) PROG (PARI) vector(50, n, (3 +10*n +18*n^2 +8*n^3 -3*(-1)^n*(1+2*n))/48) \\ G. C. Greubel, Dec 12 2019 (MAGMA) [(3 +10*n +18*n^2 +8*n^3 -3*(-1)^n*(1+2*n))/48: n in [1..50]]; // G. C. Greubel, Dec 12 2019 (Sage) [(3 +10*n +18*n^2 +8*n^3 -3*(-1)^n*(1+2*n))/48 for n in (1..50)] # G. C. Greubel, Dec 12 2019 (GAP) List([1..50], n-> (3 +10*n +18*n^2 +8*n^3 -3*(-1)^n*(1+2*n))/48); # G. C. Greubel, Dec 12 2019 CROSSREFS Cf. A023855, A049777, A095800, A213849. Sequence in context: A090262 A190815 A006459 * A270105 A294425 A123325 Adjacent sequences:  A049775 A049776 A049777 * A049779 A049780 A049781 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 24 04:08 EST 2020. Contains 338607 sequences. (Running on oeis4.)