This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211228 #8 Sep 20 2013 11:34:45
%S A211228 1,1,2,2,3,4,5,8,8,15,13,28,21,51,34,92,55,164,89,290,144,509,233,888,
%T A211228 377,1541,610,2662,987,4580,1597,7852,2584,13419,4181,22868,6765,
%U A211228 38871,10946,65920,17711
%N A211228 Shallow diagonal sums of A211226.
%C A211228 The even-indexed terms a(2*n) count the compositions of n+2 into odd parts while the odd-indexed terms a(2*n+3) count the total number of parts in the compositions of n+2 into odd parts.
%F A211228 Let f(n) := (floor(n/2))! and define c(n,k) = f(n)/(f(k)*f(n-k)) = A211226(n,k). Then a(n) = sum {k = 0..floor(n/2)} c(n-k,k).
%F A211228 a(2*n) = A000045(n+2); a(2*n-1) = A029907(n).
%F A211228 O.g.f.: (1+x-2*x^4-x^5-x^6)/(1-x^2-x^4)^2 = 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + ....
%e A211228 The compositions of 5 into odd parts are 1+1+1+1+1, 1+1+3, 1+3+1, 3+1+1 and 5. Hence a(6) = 5 and a(9) = 15.
%Y A211228 Cf. A000045, A029907, A211226.
%K A211228 nonn,easy
%O A211228 0,3
%A A211228 _Peter Bala_, Apr 05 2012