cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A089903 Sum of digits of numbers between 0 and (1/9)*(10^n-1).

Original entry on oeis.org

0, 1, 48, 960, 14572, 195684, 2456796, 29567908, 345679020, 3956790132, 44567901244, 495679012356, 5456790123468, 59567901234580, 645679012345692, 6956790123456804, 74567901234567916, 795679012345679028
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089904, A089905, A089906, A087330, A089907, A089908, A089909, A034967.

Programs

  • Mathematica
    LinearRecurrence[{22,-141,220,-100},{0,1,48,960},20] (* Harvey P. Dale, May 12 2023 *)

Formula

a(n) = s(1, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (-88*(-1+10^n)+9*(16+9*10^n)*n)/162. G.f.: x*(45*x^2+26*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

A089904 Sum of digits of numbers between 0 and (2/9)*(10^n-1).

Original entry on oeis.org

0, 3, 109, 2055, 30501, 404947, 5049393, 60493839, 704938285, 8049382731, 90493827177, 1004938271623, 11049382716069, 120493827160515, 1304938271604961, 14049382716049407, 150493827160493853
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089903, A089905, A089906, A087330, A089907, A089908, A089909, A034967.

Formula

a(n) = s(2, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (-77*(-1+10^n)+9*(14+9*10^n)*n)/81. G.f.: x*(80*x^2+43*x+3) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

A089906 Sum of digits of numbers between 0 and (4/9)*(10^n-1).

Original entry on oeis.org

0, 10, 270, 4650, 66430, 864210, 10641990, 126419770, 1464197550, 16641975330, 186419753110, 2064197530890, 22641975308670, 246419753086450, 2664197530864230, 28641975308642010, 306419753086419790
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089903, A089904, A089905, A087330, A089907, A089908, A089909, A034967.

Formula

a(n) = s(4, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (2*(-55*(-1+10^n)+9*(10+9*10^n)*n))/81. G.f.: 10*x*(12*x^2+5*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

A089907 Sum of digits of numbers between 0 and (6/9)*(10^n-1).

Original entry on oeis.org

0, 21, 483, 7785, 107787, 1377789, 16777791, 197777793, 2277777795, 25777777797, 287777777799, 3177777777801, 34777777777803, 377777777777805, 4077777777777807, 43777777777777809, 467777777777777811
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089903, A089904, A089905, A087330, A089906, A089908, A089909, A034967.

Programs

  • Mathematica
    LinearRecurrence[{22,-141,220,-100},{0,21,483,7785},20] (* Harvey P. Dale, Aug 22 2022 *)

Formula

a(n) = s(6, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (-11/9*(-1+10^n)+(2+3*10^n)*n). G.f.: 3*x*(40*x^2+7*x+7) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

A089908 Sum of digits of numbers between 0 and (7/9)*(10^n-1).

Original entry on oeis.org

0, 28, 609, 9555, 130501, 1654947, 20049393, 235493839, 2704938285, 30549382731, 340493827177, 3754938271623, 41049382716069, 445493827160515, 4804938271604961, 51549382716049407, 550493827160493853
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089903, A089904, A089905, A087330, A089906, A089907, A089909, A034967.

Formula

a(n) = s(7, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (7*(-22*(-1+10^n)+9*(4+9*10^n)*n))/162. G.f.: 7*x*(15*x^2-x+4) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

A089909 Sum of digits of numbers between 0 and (8/9)*(10^n-1).

Original entry on oeis.org

0, 36, 748, 11460, 154572, 1945684, 23456796, 274567908, 3145679020, 35456790132, 394567901244, 4345679012356, 47456790123468, 514567901234580, 5545679012345692, 59456790123456804, 634567901234567916
Offset: 0

Views

Author

Benoit Cloitre, Nov 14 2003

Keywords

Comments

From a suggestion of Yalcin Aktar

Links

Crossrefs

Cf. A089903, A089904, A089905, A087330, A089906, A089907, A089908, A034967.

Formula

a(n) = s(8, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (4*(-11*(-1+10^n)+9*(2+9*10^n)*n))/81. G.f.: 4*x*(20*x^2-11*x+9) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013
Showing 1-6 of 6 results.

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