The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A219615 a(n) = Sum_{k=0..12} binomial(n,k). 2
 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8191, 16369, 32647, 64839, 127858, 249528, 480492, 910596, 1695222, 3096514, 5546382, 9740686, 16777216, 28354132, 47050564, 76717268, 123012781, 194129627, 301766029, 462411533, 699030226, 1043243132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of compositions (ordered partitions) of n+1 into thirteen or fewer parts. a(n) is the sum of the first thirteen terms in the n-th row of Pascal's triangle. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1). FORMULA a(n) = (n^12 - 54n^11 + 1397n^10 - 21450n^9 + 218823n^8 - 1508562n^7 + 7374191n^6 - 23551110n^5 + 58206676n^4 - 48306984n^3 + 173699712n^2 + 312888960n)/479001600. - Charles R Greathouse IV, Nov 27 2012 a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=16, a(5)=32, a(6)=64, a(7)=128, a(8)=256, a(9)=512, a(10)=1024, a(11)=2048, a(12)=4096, a(n)= 13*a(n-1)- 78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+ 1716*a(n-7)- 1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - Harvey P. Dale, Nov 29 2012 EXAMPLE a(13)= 8191 because there are (2^13) -1 compositions of 14 into thirteen or fewer parts. When 1<= n <= 12, for n=5, a(5) = 2*a(4) = 2*16 = 32. For n=12, a(12) = 2*a(11)= 2*2048 = 4096. When n>12, for n=13, a(13) = 2*a(12) - binomial(12,12) = 2*4096 - 1 = 8191. For n = 15, a(15) = 2*a(14) - binomial(14,12) = 2*16369 - 91 = 32738 - 91 = 32647. MATHEMATICA Table[Sum[Binomial[n, k], {k, 0, 12}], {n, 0, 40}] (* T. D. Noe, Nov 27 2012 *) LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096}, 40] (* Harvey P. Dale, Nov 29 2012 *) PROG (PARI) a(n)=sum(k=1, 12, binomial(n, k)) \\ Charles R Greathouse IV, Nov 27 2012 CROSSREFS Cf. A000127, A006261, A008859, A008860, A008861, A008862, A008863, A219531. Sequence in context: A219531 A168083 A221180 * A168084 A133025 A216095 Adjacent sequences:  A219612 A219613 A219614 * A219616 A219617 A219618 KEYWORD nonn,easy AUTHOR Mokhtar Mohamed, Nov 23 2012 EXTENSIONS Sequence corrected and extended by T. D. Noe, Nov 26 2012 Definition corrected by Harvey P. Dale, Nov 29 2012 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 June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)