Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Nov 30 2019 06:10:44
%S 12,142,835,5798,124932,853467,6536382,50852019,1234849644,9043402501,
%T 73007772802,593742784829,4859761676391,125320157443726,
%U 953467954114363,7939655757745265,66368199913921497,556704809728838604,4684478925507420069,125076091920076709793
%N Sum of all n-digit terms of A005043.
%e Sum of all 1-digit Riordan numbers is 1 + 0 + 1 + 1 + 3 + 6 = 12.
%e Sum of all 2-digit Riordan numbers is 15 + 36 + 91 = 142.
%e Sum of all 3-digit Riordan numbers is 232 + 603 = 835.
%t digNum[n_] := Length @ IntegerDigits[n];rio[0] = 1; rio[1] = 0; rio[n_] := rio[n] = (n - 1)*(2*rio[n - 1] + 3*rio[n - 2])/(n + 1); digCount = 0; sum = 0; cumsum = {}; Do[r = rio[n]; If[digNum[r] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += r, {n, 0, 50}]; Differences[cumsum] (* _Amiram Eldar_, Nov 30 2019 *)
%Y Cf. A005043.
%K nonn,base,less
%O 1,1
%A _Parthasarathy Nambi_, Dec 06 2007
%E More terms from _Amiram Eldar_, Nov 30 2019