A065025 Consider biquanimous numbers that exclude 0's; sequence gives number of n-digit non-biquanimous numbers - number of n-digit biquanimous numbers.

9, 63, 513, 3423, 18589, 73035, 225479, 617215, 1622001, 4300263, 12128763, 37076783, 122411649, 427600575, 1550703157, 5759666431, 21738733961, 82999762711, 319722139579, 1240393764207, 4840363237201, 18979321319087, 74713018378209, 295061102101311

Offset: 1

Author

N. J. A. Sloane, Nov 03 2001

Keywords

• nonn
• base
• easy

Comments

A biquanimous number (A064544) is a number whose digits can be split into two groups with equal sums.

References

• William P. Thurston, personal communication.
• William P. Thurston, Biquanimous Generating Function, math-fun mailing list, November 2001.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1660
• Index entries for linear recurrences with constant coefficients, signature (17, -114, 348, -228, -1524, 3888, -216, -11046, 11382, 12012, -26544, 84, 28812, -13152, -15816, 13407, 3201, -5834, 628, 984, -288).

Crossrefs

Cf. A064544, A065023, A065024, A288550.

Formula

From Alois P. Heinz, Jun 12 2017: (Start)

G.f.: -x*(988416*x^33 +272448*x^32 -6983328*x^31 -2873424*x^30 [phone]*x^29 [phone]*x^28 -33545700*x^27 -25677164*x^26 [phone]*x^25 [phone]*x^24 -7032026*x^23 -11748538*x^22 -12593064*x^21 -17118040*x^20 [phone]*x^19 [phone]*x^18 -32880510*x^17 -15770937*x^16 [phone]*x^15 -4824040*x^14 -21307320*x^13 [phone]*x^12 +7474762*x^11 -5162898*x^10 -999324*x^9 +1008806*x^8 +39654*x^7 -89810*x^6 +3200*x^5 +992*x^4 +1248*x^3 -468*x^2 +90*x -9) / ((4*x-1) *(3*x-1)^2 *(2*x-1)^3 *(x+1)^7 *(x-1)^8).

a(n) = 9^n - 2 * A288550(n). (End)

Extensions

New offset and 4 more terms from Alois P. Heinz, Jun 11 2017