The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A134481 Row sums of triangle A134480. 4
 1, 5, 20, 50, 100, 175, 280, 420, 600, 825, 1100, 1430, 1820, 2275, 2800, 3400, 4080, 4845, 5700, 6650, 7700, 8855, 10120, 11500, 13000, 14625, 16380, 18270, 20300, 22475, 24800, 27280, 29920, 32725, 35700, 38850, 42180, 45695 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of [1, 4, 11, 4, 1, -1, 1, -1, 1, -1, ...]. Also, 1 followed by 5 * A000292, the tetrahedral numbers; i.e., 1, then 5 * (1, 4, 10, 25, 35, ...). If Y is a 5-subset of an n-set X then, for n>=8, a(n-7) is the number of 4-subsets of X having exactly one element in common with Y. - Milan Janjic, Dec 28 2007 LINKS Vincenzo Librandi, 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) = 5*binomial(n+2,3) for n>0. - Milan Janjic, Dec 28 2007 G.f.: 1 + 5*x / (1-x)^4. - R. J. Mathar, Apr 04 2012 a(n) = Sum_{i=0..n} (n+i)*(1+i) for n > 0. - Bruno Berselli, Dec 16 2013 E.g.f.: 1 + 5*exp(x)*x*(6 + 6*x + x^2)/6. - Stefano Spezia, Oct 09 2023 EXAMPLE a(2) = 20 = sum of row 3 terms of triangle A134480: (9 + 7 + 4). a(3) = 50 = (1, 3, 3, 1) dot (1, 4, 11, 4) = (1 + 12 + 33 + 4). a(2) = 20 = 2*1 + 3*2 + 4*3; a(5) = 5*1 + 6*2 + 7*3 + 8*4 + 9*5 + 10*6. - Bruno Berselli, Dec 16 2013 MATHEMATICA CoefficientList[Series[1+5x/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *) PROG (Magma) I:=[1, 5, 20, 50, 100]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012 CROSSREFS Cf. A134480, A000292. Sequence in context: A147488 A297569 A190094 * A358632 A062158 A034133 Adjacent sequences: A134478 A134479 A134480 * A134482 A134483 A134484 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Oct 27 2007 STATUS approved

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

Last modified December 2 13:39 EST 2023. Contains 367524 sequences. (Running on oeis4.)