This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054446 Triangle of partial row sums of triangle A037027(n,m), n >= m >= 0 (Fibonacci convolution triangle). 2
 1, 2, 1, 5, 3, 1, 12, 9, 4, 1, 29, 24, 14, 5, 1, 70, 62, 42, 20, 6, 1, 169, 156, 118, 67, 27, 7, 1, 408, 387, 316, 205, 100, 35, 8, 1, 985, 951, 821, 588, 332, 142, 44, 9, 1, 2378, 2323, 2088, 1614, 1020, 509, 194, 54, 10, 1, 5741, 5652, 5232, 4290, 2966, 1671, 747, 257 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In the language of the Shapiro et al. reference (given in A053121) such a lower triangular (ordinary) convolution array, considered as a matrix, belongs to the Riordan-group. The G.f. for the row polynomials p(n,x) (increasing powers of x) is Pell(z)/(1-x*z*Fib(z)) with Pell(x)=1/(1-2*x-x^2) = g.f. for A000129(n+1) (Pell numbers without 0) and Fib(x)=1/(1-x-x^2) = g.f. for A000045(n+1) (Fibonacci numbers without 0). LINKS FORMULA a(n, m)=sum(A037027(n, k), k=m..n), n >= m >= 0, a(n, m) := 0 if n= m >= 0, a(n, m) := 0 if n= 0, with Fib(x) = g.f. A000045(n+1) and Pell(x) = g.f. A000129(n+1). T(n,0) = 2*T(n-1,0) + T(n-2,0), T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k) for k>0, T(0,0) = 1, T(1,0) = 2, T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 26 2014 EXAMPLE {1}; {2,1}; {5,3,1}; {12,9,4,1};... Fourth row polynomial (n=3): p(3,x)= 12+9*x+4*x^2+x^3 CROSSREFS Cf. A037027, A000045, A000129. Row sums: A054447(n). Sequence in context: A120095 A130197 A106513 * A164981 A047858 A125171 Adjacent sequences:  A054443 A054444 A054445 * A054447 A054448 A054449 KEYWORD easy,nonn,tabl AUTHOR Wolfdieter Lang, Apr 27 2000 and May 08 2000 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 January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)