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A080151
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Let m = Wonderful Demlo number A002477(n); a(n) = sum of digits of m.
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9
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1, 4, 9, 16, 25, 36, 49, 64, 81, 82, 85, 90, 97, 106, 117, 130, 145, 162, 163, 166, 171, 178, 187, 198, 211, 226, 243, 244, 247, 252, 259, 268, 279, 292, 307, 324, 325, 328, 333, 340, 349, 360, 373, 388, 405, 406, 409, 414, 421, 430, 441, 454, 469, 486, 487
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OFFSET
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1,2
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n) = (9^2)*(n/9 - {n/9} + {n/9}^2) = 81*(floor(n/9) + {n/9}^2), where the symbol {n} means fractional part of n. - Enrique Pérez Herrero, Nov 22 2009
Empirical g.f.: x*(17*x^8 + 15*x^7 + 13*x^6 + 11*x^5 + 9*x^4 + 7*x^3 + 5*x^2 + 3*x + 1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Mar 05 2014
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MAPLE
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f := n -> 9*n - 81*frac(1/9*n) + 81*frac(1/9*n)^2:
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MATHEMATICA
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(* by direct counting *)
Repunit[n_] := (-1 + 10^n)/9; A080151[n_]:=Plus @@ IntegerDigits[Repunit[n]^2];
(* by the formula * )
A080151[n_] := (9^2)*(n/9 - FractionalPart[n/9] + FractionalPart[n/9]^2)
(* or alternatively *)
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PROG
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(Haskell) a n=(div n 9)*81+(mod n 9)^2
(PARI) vector(100, n, (n\9)*81+(n%9)^2) \\ Colin Barker, Mar 05 2014
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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