A133211 Sum of all n-digit Perrin numbers.

27, 338, 3113, 29524, 280003, 3619458, 33362676, 316408590, 3000790339, 28459223116, 367878072268, 3390948851403, 32159451022886, 304997313558856, 2892566829325533, 37390757461695633, 344652632558806213, 3268654274185743387, 30999620356388134160, 293997584825511430878

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Perrin Sequence.

Example

Sum of all 1-digit Perrin numbers = 3 + 0 + 2 + 3 + 2 + 5 + 5 + 7 = 27.
Sum of all 2-digit Perrin numbers = 10 + 12 + 17 + 22 + 29 + 39 + 51 + 68 + 90 = 338.
Sum of all 3-digit Perrin numbers = 119 + 158 + 209 + 277 + 367 + 486 + 644 + 853 = 3113.

Mathematica

a[n_] := a[n] = a[n - 2] + a[n - 3]; a[0] = 3; a[1] = 0; a[2] = 2; t = Table[a@n, {n, 0, 150}]; Table[Plus @@ Select[t, 10^(n - 1) -1 < # < 10^n &], {n, 18}] - Robert G. Wilson v, Oct 14 2007
With[{pernos=LinearRecurrence[{0, 1, 1}, {3, 0, 2}, 200]}, Table[Total[ Select[ pernos, IntegerLength[#]==n&]], {n, 20}]] (* Harvey P. Dale, Apr 20 2012 *)

Crossrefs

Cf. A001608.

Sequence in context: A160223 A182668 A076394 * A178983 A029947 A030673

Adjacent sequences: A133208 A133209 A133210 * A133212 A133213 A133214

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Oct 11 2007

Extensions

More terms from Robert G. Wilson v, Oct 14 2007

More terms from Amiram Eldar, Nov 30 2019

Status

approved