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a(n) = n*A010888(n).
1

%I #20 Apr 24 2023 02:01:34

%S 0,1,4,9,16,25,36,49,64,81,10,22,36,52,70,90,112,136,162,19,40,63,88,

%T 115,144,175,208,243,28,58,90,124,160,198,238,280,324,37,76,117,160,

%U 205,252,301,352,405,46,94,144,196,250,306,364,424,486,55,112,171,232

%N a(n) = n*A010888(n).

%C 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).

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

%F 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).

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

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

%F a(A017173(n)) = A017173(n).

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

%o (Python)

%o def A361203(n): return n*(1 + (n - 1) % 9) # _Chai Wah Wu_, Apr 23 2023

%Y Cf. A010888, A017173, A057147.

%K nonn,base,easy

%O 0,3

%A _Stefano Spezia_, Apr 20 2023