A361203 a(n) = n*A010888(n).

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 22, 36, 52, 70, 90, 112, 136, 162, 19, 40, 63, 88, 115, 144, 175, 208, 243, 28, 58, 90, 124, 160, 198, 238, 280, 324, 37, 76, 117, 160, 205, 252, 301, 352, 405, 46, 94, 144, 196, 250, 306, 364, 424, 486, 55, 112, 171, 232

Offset: 0

Author

Stefano Spezia, Apr 20 2023

Keywords

• nonn
• base
• easy

Comments

Every run of increasing terms ends with a positive multiple of 81, and except for the first run, it starts with a term of A017173 which is a fixed point for this sequence (see 4th formula).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A010888, A017173, A057147.

Programs

Mathematica

a[n_]:=n(n - 9*Floor[(n-1)/9]); Join[{0},Array[a,58]]

Python

def A361203(n): return n*(1 + (n - 1) % 9) # Chai Wah Wu, Apr 23 2023

Formula

G.f.: x*(1 + 4*x + 9*x^2 + 16*x^3 + 25*x^4 + 36*x^5 + 49*x^6 + 64*x^7 + 81*x^8 + 8*x^9 + 14*x^10 + 18*x^11 + 20*x^12 + 20*x^13 + 18*x^14 + 14*x^15 + 8*x^16)/((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2).

a(n) = 2*a(n-9) - a(n-18) for n > 17.

a(n) = n*(n - 9*floor((n-1)/9)) for n > 0.

a(A017173(n)) = A017173(n).