|
Search: id:A051679
|
|
|
| A051679 |
|
Total number of even entries in first n rows of Pascal's triangle. |
|
+0
1
|
|
| 0, 0, 1, 1, 4, 6, 9, 9, 16, 22, 29, 33, 42, 48, 55, 55, 70, 84, 99, 111, 128, 142, 157, 165, 186, 204, 223, 235, 256, 270, 285, 285, 316, 346, 377, 405, 438, 468, 499, 523, 560, 594, 629, 657, 694, 724, 755, 771, 816, 858, 901, 937, 982, 1020, 1059, 1083, 1132
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Source
Index entries for sequences generated by sieves
|
|
FORMULA
|
a(0)=a(1)=0, a(2n) = 3a(n)+n(n-1)/2, a(2n+1) = 2a(n)+a(n+1)+n(n+1)/2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 10 2003
n(n+3)/2 - A074330(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 10 2003
|
|
MATHEMATICA
|
f[n_] := n + 1 - Sum[ Mod[ Binomial[n, k], 2], {k, 0, n} ]; Table[ Sum[ f[k], {k, 0, n} ], {n, 0, 100} ]
|
|
PROGRAM
|
(PARI) a(n)=if(n<2, 0, if(n%2==0, 3*a(n/2)+n/4*(n/2-1), 2*a((n-1)/2)+a((n+1)/2)+((n-1)/4)*((n+1)/2)))
|
|
CROSSREFS
|
A006046, A048967.
Sequence in context: A084335 A094115 A163297 this_sequence A010378 A166593 A124785
Adjacent sequences: A051676 A051677 A051678 this_sequence A051680 A051681 A051682
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
|
|
|
Search completed in 0.002 seconds
|
