A341193 -id:A341193 - cp's OEIS frontend

A341191 Number of ways to write n as an ordered sum of 2 nonzero decimal palindromes.

1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 7, 6, 5, 4, 3, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 7, 2, 2

Offset: 2

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 2..20000

Cf. A002113, A136522, A260254, A319468, A341155, A341192, A341193.

nmax = 90; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^2, {x, 0, nmax}], x] // Drop[#, 2] &

A341192 Number of ways to write n as an ordered sum of 3 nonzero decimal palindromes.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 36, 45, 52, 60, 66, 70, 72, 72, 70, 66, 60, 55, 45, 39, 34, 30, 27, 25, 24, 24, 24, 27, 27, 25, 27, 27, 27, 27, 27, 27, 27, 27, 30, 27, 27, 30, 30, 30, 30, 30, 30, 30, 30, 33, 27, 30, 33, 33, 33, 33, 33, 33, 33, 33, 36, 27, 34, 36, 36, 36, 36

Offset: 3

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 3..20000

Cf. A002113, A136522, A261131, A261132, A261422, A341156, A341191, A341193.

nmax = 70; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x] // Drop[#, 3] &

A341184 Number of ways to write n as an ordered sum of 5 nonzero decimal palindromes.

Original entry on oeis.org

1, 5, 15, 35, 70, 126, 210, 330, 495, 710, 981, 1310, 1695, 2130, 2605, 3106, 3615, 4110, 4575, 4980, 5311, 5555, 5705, 5760, 5725, 5611, 5435, 5210, 4975, 4735, 4511, 4320, 4170, 4065, 4005, 3986, 4005, 4040, 4100, 4175, 4241, 4310, 4380, 4450, 4520, 4590, 4665, 4740, 4810

Offset: 5

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 5..10000

Cf. A002113, A136522, A319470, A341158, A341191, A341192, A341193, A341203, A341204, A341205, A341206, A341207.

nmax = 53; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

A341203 Number of ways to write n as an ordered sum of 6 nonzero decimal palindromes.

Original entry on oeis.org

1, 6, 21, 56, 126, 252, 462, 792, 1287, 1996, 2973, 4272, 5942, 8022, 10536, 13488, 16857, 20592, 24622, 28836, 33108, 37298, 41262, 44862, 47976, 50508, 52398, 53612, 54192, 54186, 53688, 52818, 51708, 50492, 49296, 48228, 47383, 46788, 46497, 46506, 46773, 47268, 47948

Offset: 6

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 6..10000

Cf. A002113, A136522, A319471, A341159, A341184, A341191, A341192, A341193, A341204, A341205, A341206, A341207.

nmax = 48; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

A341204 Number of ways to write n as an ordered sum of 7 nonzero decimal palindromes.

Original entry on oeis.org

1, 7, 28, 84, 210, 462, 924, 1716, 3003, 4998, 7966, 12222, 18123, 26054, 36408, 49560, 65835, 85470, 108591, 135163, 164976, 197632, 232547, 268968, 306005, 342678, 377979, 410914, 440630, 466417, 487788, 504511, 516621, 524412, 528409, 529320, 528003, 525308, 522144

Offset: 7

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 7..10000

Cf. A002113, A136522, A319472, A341165, A341184, A341191, A341192, A341193, A341203, A341205, A341206, A341207.

nmax = 45; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

A341205 Number of ways to write n as an ordered sum of 8 nonzero decimal palindromes.

Original entry on oeis.org

1, 8, 36, 120, 330, 792, 1716, 3432, 6435, 11432, 19392, 31592, 49652, 75552, 111624, 160512, 225093, 308352, 413232, 542424, 698146, 881912, 1094312, 1334824, 1601679, 1891800, 2200836, 2523256, 2852636, 3181936, 3503900, 3811488, 4098313, 4359048, 4589768, 4788192, 4953860

Offset: 8

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 8..10000

Cf. A002113, A136522, A319473, A341166, A341184, A341191, A341192, A341193, A341203, A341204, A341206, A341207.

nmax = 44; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.

Original entry on oeis.org

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24301, 43686, 75249, 124809, 200115, 311157, 470415, 693000, 996633, 1401436, 1929465, 2603979, 3448440, 4485267, 5734395, 7211718, 8927523, 10885050, 13079257, 15496065, 18112050, 20894757, 23803659, 26791749, 29807697, 32798448

Offset: 9

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 9..10000

Cf. A002113, A136522, A319474, A341167, A341184, A341191, A341192, A341193, A341203, A341204, A341205, A341207.

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(t<1, 0, add(`if`(p(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..43);  # Alois P. Heinz, Feb 07 2021

nmax = 43; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

A341207 Number of ways to write n as an ordered sum of 10 nonzero decimal palindromes.

Original entry on oeis.org

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48610, 92288, 167500, 292180, 491920, 802120, 1270324, 1958605, 2945800, 4329370, 6226580, 8774695, 12129890, 16464610, 21963190, 28815655, 37209766, 47321560, 59304730, 73279565, 89322100, 107454362, 127636600, 149762345, 173657020

Offset: 10

Ilya Gutkovskiy, Feb 06 2021

Alois P. Heinz, Table of n, a(n) for n = 10..10000

Cf. A002113, A136522, A319475, A341168, A341184, A341191, A341192, A341193, A341203, A341204, A341205, A341206.

nmax = 43; CoefficientList[Series[Sum[Boole[PalindromeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

cp's OEIS Frontend

A341191 Number of ways to write n as an ordered sum of 2 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341192 Number of ways to write n as an ordered sum of 3 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341184 Number of ways to write n as an ordered sum of 5 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341203 Number of ways to write n as an ordered sum of 6 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341204 Number of ways to write n as an ordered sum of 7 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341205 Number of ways to write n as an ordered sum of 8 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A341206 Number of ways to write n as an ordered sum of 9 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A341207 Number of ways to write n as an ordered sum of 10 nonzero decimal palindromes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica