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 A132156 Sum of all n-digit Stern numbers. 0

%I

%S 13,148,1003,16141,117547,917053,15502289,114274754,909482399,

%T 15471962269,115061008452,917885746619,15675637954053,116877859994048,

%U 933643385166035,15975162211603393,119196492782053456,952870691477908028,16319572144410372393,121792577413939691253

%N Sum of all n-digit Stern numbers.

%e Sum of all 1-digit Stern numbers is 1 + 1 + 2 + 3 + 6 = 13.

%e Sum of all 2-digit Stern numbers is 11 + 20 + 40 + 77 = 148.

%e Sum of all 3-digit Stern numbers is 148 + 285 + 570 = 1003.

%t stern[1] = 1; stern[n_] := stern[n] = Sum[stern[k], {k, n - Ceiling[(Sqrt[8*n -7]-1)/2], n-1}]; digNum[n_] := Length @ IntegerDigits[n]; digCount = 0; sum = 0; cumsum = {}; Do[s = stern[n]; If[digNum[s] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += s, {n, 1, 25}]; Differences[cumsum] (* _Amiram Eldar_, Nov 30 2019 *)

%Y Cf. A005230.

%K nonn,base,less

%O 1,1

%A _Parthasarathy Nambi_, Nov 01 2007

%E More terms from _Amiram Eldar_, Nov 30 2019

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Last modified December 4 09:10 EST 2021. Contains 349484 sequences. (Running on oeis4.)