A132156 Sum of all n-digit Stern numbers.

13, 148, 1003, 16141, 117547, 917053, 15502289, 114274754, 909482399, 15471962269, 115061008452, 917885746619, 15675637954053, 116877859994048, 933643385166035, 15975162211603393, 119196492782053456, 952870691477908028, 16319572144410372393, 121792577413939691253

Offset: 1

Author

Parthasarathy Nambi, Nov 01 2007

Keywords

• nonn
• base
• less

Examples

			Sum of all 1-digit Stern numbers is 1 + 1 + 2 + 3 + 6 = 13.
Sum of all 2-digit Stern numbers is 11 + 20 + 40 + 77 = 148.
Sum of all 3-digit Stern numbers is 148 + 285 + 570 = 1003.
		

Crossrefs

Cf. A005230.

Programs

Mathematica

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 *)

Extensions

More terms from Amiram Eldar, Nov 30 2019