A091582 Number of partitions of the n-th decimal palindrome.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 56, 1002, 10143, 75175, 451276, 2323520, 10619863, 44108109, 169229875, 214481126, 679903203, 2056148051, 5964539504, 16670689208, 45060624582, 118159068427, 301384802048, 749474411781, 1820701100652, 4714566886083, 10963707205259

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Partition

Formula

a(n) = A000041(A002113(n)).

Prog

(Python)
from sympy import npartitions
def A091582(n):
    if n == 1: return 1
    y = 10*(x:=10**(len(str(n>>1))-1))
    return npartitions((c:=n-x)*x+int(str(c)[-2::-1]or 0) if n<x+y else (c:=n-y)*y+int(str(c)[-1::-1]or 0)) # Chai Wah Wu, Jun 14 2024

Crossrefs

Cf. A000041, A002113, A091584, A091583.

Sequence in context: A218025 A091955 A091584 * A241727 A326465 A101977

Adjacent sequences: A091579 A091580 A091581 * A091583 A091584 A091585

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 22 2004

Extensions

a(1)=1 prepended and more terms from Georg Fischer, Dec 15 2020

Status

approved