A010735 -id:A010735 - cp's OEIS frontend

A176523 Decimal expansion of (45+3*sqrt(235))/10.

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

Offset: 1

Klaus Brockhaus, Apr 23 2010

Continued fraction expansion of (45+3*sqrt(235))/10 is A010735.

			(45+3*sqrt(235))/10 = 9.09891291502676749696...

Cf. A176524 (decimal expansion of sqrt(235)), A010735 (repeat 9, 10).

RealDigits[(45+3Sqrt[235])/10,10,120][[1]] (* Harvey P. Dale, Aug 27 2011 *)

A176536 Decimal expansion of (15 + sqrt(235))/3.

Original entry on oeis.org

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

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of (15 + sqrt(235))/3 is A010735 preceded by 10.

			(15+sqrt(235))/3 = 10.10990323891863055218...

Daniel Starodubtsev, Table of n, a(n) for n = 2..10000

Cf. A176524 (decimal expansion of sqrt(235)), A010735 (repeat 9, 10).

RealDigits[(15+Sqrt[235])/3,10,120][[1]] (* Harvey P. Dale, Feb 17 2020 *)

sqrt(235)/3 + 5 \\ Charles R Greathouse IV, Apr 25 2016

A207260 Triangle read by rows: T(n,k) = k^2 + (1-(-1)^(n-k))/2.

Original entry on oeis.org

0, 1, 1, 0, 2, 4, 1, 1, 5, 9, 0, 2, 4, 10, 16, 1, 1, 5, 9, 17, 25, 0, 2, 4, 10, 16, 26, 36, 1, 1, 5, 9, 17, 25, 37, 49, 0, 2, 4, 10, 16, 26, 36, 50, 64, 1, 1, 5, 9, 17, 25, 37, 49, 65, 81, 0, 2, 4, 10, 16, 26, 36, 50, 64, 82, 100, 1, 1, 5, 9, 17, 25, 37, 49, 65, 81, 101, 121

Offset: 0

Philippe Deléham, Feb 16 2012

Row sums are A171218(n).

			Triangle begins:
  0;
  1, 1;
  0, 2, 4;
  1, 1, 5,  9;
  0, 2, 4, 10, 16;
  1, 1, 5,  9, 17, 25;
  0, 2, 4, 10, 16, 26, 36;
  1, 1, 5,  9, 17, 25, 37, 49;
  0, 2, 4, 10, 16, 26, 36, 50, 64;
  1, 1, 5,  9, 17, 25, 37, 49, 65, 81;
  ...

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).

Cf. A000034, A000035, A000290, A002522, A007590, A010710, A010735, A080335, A171218, A137928.

/* As triangle */ [[ k^2 + (1-(-1)^(n-k))/2: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 09 2024

Table[k^2 + (1-(-1)^(n-k))/2, {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Nov 13 2024 *)

T(n+k, n) = A002522(n) if k is odd.
T(n+k, n) = n^2 = A000290(n) if k is even.
T(2*n, n) = A137928(n), n>0.
T(2*n+1, n+1) = A080335(n).
T(n,0) = A000035(n).
T(n+1,1) = A000034(n).
T(n+2,2) = A010710(n).
T(n+3,3) = A010735(n).
Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A007590(n), A000035(n), A171218(n)
for x = -1, 0, 1 respectively.
G.f.: x*(1 + y - x*y + x*(1 + 2*x)*y^2)/((1 - x^2)*(1 - x*y)^3). - Stefano Spezia, Nov 12 2024

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A176523 Decimal expansion of (45+3*sqrt(235))/10.

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A176536 Decimal expansion of (15 + sqrt(235))/3.

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A207260 Triangle read by rows: T(n,k) = k^2 + (1-(-1)^(n-k))/2.

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