|
| |
|
|
A004798
|
|
Convolution of Fibonacci numbers 1,2,3,5,... with themselves.
|
|
6
| |
|
|
1, 4, 10, 22, 45, 88, 167, 310, 566, 1020, 1819, 3216, 5645, 9848, 17090, 29522, 50793, 87080, 148819, 253610, 431086, 731064, 1237175, 2089632, 3523225, 5930668, 9968122
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2010: (Start)
a(n) is the number of subwords of the form 0000 in all binary words of length n+3 that have no pair of adjacent 1's. Example: a(2)=4 because in the 13 (=A000045(7)) binary words of length 5 that have no pair of adjacent 1's, namely 00000, 00001, 00010, 00100, 00101, 01000, 01001, 01010, 10000, 10001, 10010, 10100, 10101, we have 2 + 1 + 0 + 0 + 0 + 0 + 0 + 0 + 1 + 1 + 0 + 0 + 0 = 4 subwords of the form 0000.
a(n) = Sum(k*A171855(n + 3,k),k>=0). (End)
|
|
|
FORMULA
| O.g.f.: (x^2+2x+1)/(1-x-x^2)^2.- Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 11 2001
a(n) = a(n-1) + a(n-2) + Fibonacci(n+2). - DELEHAM Philippe, Jan 22 2012
|
|
|
EXAMPLE
| a(6) = 45 + 22 + A000045(6+2) = 45 + 22 + 21 = 88 . - DELEHAM Philippe, Jan 22 2012
|
|
|
PROG
| (Other) sage: taylor( mul((x^2*(1+x^2))/(1-x^2-x^4) for i in xrange(0, 2)), x, 0, 56)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 01 2009]
|
|
|
CROSSREFS
| A171855, A000045 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2010]
Sequence in context: A052837 A052821 A023628 * A174622 A038621 A078407
Adjacent sequences: A004795 A004796 A004797 * A004799 A004800 A004801
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
| |
|
|
