|
| |
|
|
A052905
|
|
(n^2 + 7n + 2)/2.
|
|
13
| |
|
|
1, 5, 10, 16, 23, 31, 40, 50, 61, 73, 86, 100, 115, 131, 148, 166, 185, 205, 226, 248, 271, 295, 320, 346, 373, 401, 430, 460, 491, 523, 556, 590, 625, 661, 698, 736, 775, 815, 856, 898, 941, 985, 1030, 1076, 1123, 1171, 1220, 1270, 1321, 1373, 1426, 1480
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| If Y_i (i=1,2,3,4,5) are 2-blocks of an n-set X then, for n>=10, a(n-4) is the number of (n-2)-subsets of X intersecting each Y_i (i=1,2,3,4,5). - Milan R. Janjic (agnus(AT)blic.net), Nov 09 2007
|
|
|
LINKS
| Milan Janjic, Two Enumerative Functions
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 884
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
| G.f.: (-2*x+2*x^2-1)/(-1+x)^3
Recurrence: {a(0)=1, a(1)=5, a(2)=10, -2*a(n)+n^2+7*n+2}
1/2*n^2+7/2*n+1
Starting 1, 5, 10, 16, 23,... gives binomial transform of (1, 4, 1, 0, 0, 0,...). A052905 = row sums of triangle A131899 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 25 2007
Row sums of triangle A134199 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 13 2007
a(n)=n+a(n-1)+3 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
|
|
|
EXAMPLE
| a(1)=1+1+3=5; a(2)=2+5+3=10; a(3)=3+10+3=16; a(4)=4+16+3=23 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
|
|
|
MAPLE
| spec := [S, {S=Prod(Sequence(Z), Sequence(Z), Union(Sequence(Z), Z, Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(binomial(n, 2)-5, n=4..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 13 2007
a:=n->sum((n-4)/2, j=0..n): seq(a(n)-2, n=5..56); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007
with (combinat):seq((fibonacci(3, n)+n-11)/2, n=3..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
a:=n->sum(k, k=0..n):seq(a(n)/2+sum(k, k=5..n)/2, n=3..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 10 2008
|
|
|
MATHEMATICA
| i=4; s=1; lst={s}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 30 2008 *)
k = 3; NestList[(k++; # + k) &, 1, 45] (* From Robert G. Wilson v, Feb 03 2011 *)
Table[(n^2 + 7n + 2)/2, {n, 0, 49}] (* From Alonso del Arte, Feb 03 2011 *)
|
|
|
PROG
| (PARI) a(n)=n*(n+7)/2+1 \\ Charles R Greathouse IV, Nov 20 2011
|
|
|
CROSSREFS
| Cf. A131899, A134199, A002522.
Sequence in context: A178181 A075003 A005280 * A194275 A026059 A115002
Adjacent sequences: A052902 A052903 A052904 * A052906 A052907 A052908
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 08 2000
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Jul 25 2010
|
| |
|
|
