The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102169 a(n) = the number of sequences of n integers such that each integer is in the range 0..4 and the sum of the integers is in the range 0..24. 2
 5, 25, 125, 625, 3125, 15625, 78005, 384550, 1829850, 8209410, 34219650, 131875900, 470597480, 1562441800, 4855374080, 14208711350, 39381411950, 103917328350, 262270328730, 635683810740, 1484963848500, 3353799866500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Changing 4 to 2 and 24 to 3 gives A105163. - Don Reble, Aug 14 2012 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 FORMULA From Michael David Hirschhorn, Aug 10 2012: (Start) a(n) is the sum of the coefficients of 1, x, x^2, ..., x^24 in (1+x+x^2+x^3+x^4)^n = (1-x^5)^n/(1-x)^n. But this is equal to the coefficient of x^24 in (1-x^5)^n/(1-x)^(n+1) = Sum_{k=0..n} (-1)^k binomial(n,k) x^5k times Sum_{m>=0} binomial(n+m,m) x^m. Hence a(n) = Sum_{k=0..4} (-1)^k binomial(n,k) binomial(n+24-5k,n). For example, if n=2, a(2) = 325-420+120 = 25. (End) G.f.: -x*(x^24 -25*x^23 +300*x^22 -2300*x^21 +12650*x^20 -53060*x^19 +175980*x^18 -472300*x^17 +1042375*x^16 -1915575*x^15 +2962780*x^14 -3894200*x^13 +4384980*x^12 -4251000*x^11 +3547700*x^10 -2533840*x^9 +1532975*x^8 -776575*x^7 +325880*x^6 -111900*x^5 +30750*x^4 -6500*x^3 +1000*x^2 -100*x +5) / (x-1)^25. - Colin Barker, Nov 01 2014 EXAMPLE a(2)=25 because there are five choices for either integer. MATHEMATICA Table[Sum[(-1)^k * Binomial[n, k] * Binomial[n+24-5k, n], {k, 0, 4}], {n, 1, 20}]  (* Vaclav Kotesovec, Nov 01 2014 after Michael David Hirschhorn *) CROSSREFS Cf. A105163. Sequence in context: A216126 A335506 A129066 * A060391 A000351 A050735 Adjacent sequences:  A102166 A102167 A102168 * A102170 A102171 A102172 KEYWORD nonn,easy AUTHOR Tony Berard (TheMathDude(AT)worldnet.att.net), Feb 16 2005 EXTENSIONS Edited by Don Reble, Mar 19 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)